Question

A bumper cart has a mass of 200 kg and has a protective bumper around it that behaves like a spring. The spring constant is 5000 n/m. If the cart is moving at a speed of 8 m/s towards a solid barrier, and upon impact, is momentarily brought to rest.

a) How much elastic potential energy will be stored in the spring when it is fully compressed?

b) What is the average force exerted by the spring if it is compressed by a distance of 0.2 meters?

Answer 1

Part A:
For this part we’re assuming all the kinetic energy of the moving bumper car is converted into elastic potential energy in the spring since the car is brought to rest. Therefore you can find the total kinetic energy to get your answer:

KE = ½ mv^2
KE = ½ (200)(8)^2
KE = 6400 J

Part B:
Now you can use Hooke’s law to find the force:

F = kx
F = (5000)(0.2)
F = 1000 N